Thank you Matthias for the information, these have helped me already a lot.

Now I have tried about a PrecisionModell that the Linestrings intersect the 
generated Point of the Intersection. The PrecisionModell was set that the 
geometries had no decimal places. However, this time the Linestrings do not 
intersect the point from the intersection. I thought the PrecisionModel is for 
such problems?!

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